A person buys a lottery ticket in 50 lotteries, in each of which his chance of winning a prize is `1/(100)`. What is the probability that he will win a prize(a) at least once (b) exactly once (c) at least twice?

Explanation

(b) `p(1)= .^50C_1(1/100)(99/100)^49= 1/2(99/100)^49`

(a) `P= .^50C_1(1/100)(99/100)^49 + .^50C_2(1/100)^2(99/100)^48 ...... .^50C_50(1/100)^500 (99/100)^0 `

`= (1/100 + 99/100)^50 - .^50C_0(99/100)^50`

`= 12- 50(99/100)^50`

(c) `p= 1 - .^50C_0(1/100)^0(99/100)^50 - .^50C_1(1/100)(99/100)^49`

Answer